Jintao Cui
Multigrid Methods for Two-Dimensional Maxwell's Equations on Graded Meshes

Institute for Mathematics and Its Applications
University of Minnesota
114 Lind Hall
207 Church St SE
Minneapolis
MN 55455
jcui@ima.umn.edu

In this work we investigate the numerical solution for two-dimensional Maxwell's equations on graded meshes. The approach is based on the Hodge decomposition. The solution $\boldsymbol{u}$ of Maxwell's equations is approximated by solving standard second order elliptic problems. The quasi-optimal error estimates for both $\boldsymbol{u}$ and $\nabla \times \boldsymbol{u}$ in the $L_2$ norm are obtained on graded meshes. We prove the uniform convergence of the $W$-cycle and full multigrid algorithms for the resulting discrete problem. The performance of these methods is illustrated by numerical results.